Question: Simplify the following expression: $y = \dfrac{6a^2 - 12a - 144}{a - 6} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $6$ , so we can rewrite the expression: $ y =\dfrac{6(a^2 - 2a - 24)}{a - 6} $ Then we factor the remaining polynomial: $a^2 {-2}a {-24} $ ${-6} + {4} = {-2}$ ${-6} \times {4} = {-24}$ $ (a {-6}) (a + {4}) $ This gives us a factored expression: $\dfrac{6(a {-6}) (a + {4})}{a - 6}$ We can divide the numerator and denominator by $(a + 6)$ on condition that $a \neq 6$ Therefore $y = 6(a + 4); a \neq 6$